Find the first partial derivatives of $\displaystyle f(x,y,z) = z \ \arctan\left(\frac{-y}{3x}\right)$.

Caution: ay/bx and ay/(bx) are very different, the former equals axy/b. Parentheses are your friends!

A. $\displaystyle \frac{\partial f}{\partial x} =$

B. $\displaystyle \frac{\partial f}{\partial y} =$

C. $\displaystyle \frac{\partial f}{\partial z} =$